Facing scrutiny over its manufacturing capability, Tesla said Tuesday that production of its Model 3 electric car is increasing so rapidly the pace may soon "exceed even that of Ford and the Model T."

The statement — featuring a dose of Tesla's characteristic swagger — comes amid mounting questions about whether the company is capable of accelerating production in order to fulfill a backlog of orders while maintaining quality standards.

Seeking to counter a chorus of critics who have questioned Tesla CEO Elon Musk's leadership in recent weeks, the automaker compared itself to Henry Ford's production line, which the made automaker based in Dearborn, Mich., famous a century ago.

"This is the fastest growth of any automotive company in the modern era," Tesla said.

Musk himself took over production of the Model 3 in recent days as the company navigates the difficult terrain of launching an all-new model.

"Car biz is hell," Musk said Monday on Twitter.

The company also said notably that it "does not require" any additional capital in 2018 through a sale of stock or issuance of debt. That may come as a relief for investors worried that the company could dilute their shares in pursuit of cash to offset heavy losses.

ELON MUSK - BUSINESS WOES
This file photo taken in 2017 shows billionaire tech entrepreneur Elon Musk, founder of the Tesla electric car company and the SpaceX aerospace exploration firm, speaking at the 2017 International Astronautical Congress 2017 in Australia.
PETER PARKS, AFP/Getty Images

Indeed, Tesla's stock had jumped more than 5% to about $267 in early afternoon trading. The shares had fallen sharply in recent weeks amid scrutiny of the company's manufacturing and over a deadly crash in California that raised concerns about the safety of the company's Autopilot partial self-driving system.

"They face formidable challenges," Autotrader analyst Michelle Krebs said.

The company said it made 9,766 Model 3 vehicles in the first quarter, reflecting a four-fold increase from the fourth. Significantly, Tesla said it expects to make 2,000 over the next seven days, which it said "is a testament to the ability of the Tesla production team."

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Tesla said it would reach 5,000 vehicles a week "in about three months." The company had originally said it would reach that pace by the end of 2017 and then later delayed it to the end of the second quarter.

To be sure, questions remain about the quality and durability of the Model 3. Some customers have reported basic problems with their cars, though automakers are commonly plagued by imperfections in early production before they work the bugs out.

Tesla countered that its internal metrics indicate customers have given the Model 3 the "highest score in Tesla's history" for initial quality. 

In the first quarter, Tesla delivered a total of 29,980 vehicles: 11,730 Model S sedans, 10,070 Model X crossovers and 8,180 Model 3 cars.

Reservations for the Model 3 are "stable" despite some cancellations "almost entirely due to delays in production in general and delays in availability of certain planned options," including the cheapest model, Tesla said.

Follow USA TODAY reporter Nathan Bomey on Twitter @NathanBomey.